I'm moving across the country next year for school, and figured it'd be a good time to start planning out how I'm going to move my framed prints (I have three at the moment, might have framed a 4th by then). What's the best way to do that? Any particular companies who are really reliable with this kind of thing? While I'd like competitive pricing, I'm expecting to pay a pretty penny to move these things, so money isn't a huge obstacle.

Are you driving at all or are you having everything moved in a truck? You could get a hold of an art moving company. It costs a very pretty penny to ship work, especially if you have glass in the frame instead of plexi. https://www.saatchiart.com/packaging

That's a pretty good link to explain the basics. Although if you do have glass in the frame instead of plexi, I highly suggest switching to plexi. It is less likely to damage your prints and obviously less likely to break. it costs a bit more than glass, but you can get it custom cut for the frame. although, if you are driving, i would package it according to that website and bring it in your car. I moved across the US using a pod and kept a lot of work in frames. None of them broke, but I also use plexiglass. I wrap them in bubble wrap and build a cardboard box to put it in.